Unless otherwise indicated herein, approaches described in this section are not prior art to the claims listed below and are not admitted as prior art by inclusion in this section.
A wireless communication device needs to be uniquely identified by other devices (e.g., base stations) by transmitting a signature sequence so that multiple devices in a wireless communication network need to be identified unambiguously. Thus, the design of a large number of uniquely identifiable signature sequences is of paramount importance. Specifically, the uniqueness of each sequence needs to be preserved after passing through the time-frequency selective wireless channel. However, there may be occasions in which the number of sequences generated in a conventional manner is not enough for the number of wireless communication devices in the system. For example, insufficient number of sequences may occur when any of the following condition exists: (1) the channel having very large delay-Doppler spread that limits the number of sequences; (2) the wireless communication devices being not synchronous in time, thereby cyclic time shift resulting in ambiguity; (3) the sequence length being limited by available resources; and (4) large number of wireless communication devices being active in the system, such as massive Machine Type Communication (mMTC). Moreover, for a large number of wireless communication devices, complexity of detection of sequences can become very high.